Quick Quiz Consider a football coach pacing back and forth along the sidelines. The diagram below shows several of coach's positions at various times. At each marked position, the coach makes a "U-turn" and moves in the opposite direction. In other words, the coach moves from position A to B to C to D. What is the coach's average speed and average velocity?

Representing Motion Using Graphs Position-Time Graphs Velocity-Time Graphs

position-time graphs a graph describing the motion of an object, with position on the vertical axis and time on the horizontal axis it is important to understand how the shape of a p-t graph relates to the motion it describes

straight line  the object is covering an equal distance per time interval (constant motion) curved line  the distance covered each time interval is not consistent (non-uniform motion)

flat line  no change in position over time (standing still) steep line  large change in position over time (moving quickly) shallow line  small change in position over time (moving slowly)

negative/downward line  the object is travelling in a negative direction can be uniform or non-uniform can be fast or slow *Therefore, by looking at a position- time graph, one can determine: the direction of movement the speed of the movement (slow or fast) if the movement is uniform (constant speed) or non-uniform (acceleration)

slope slope is the measure of the steepness of a line slope = rise = Δd = d2 - d1 run Δt t2 – t1 the slope of a p-t graph yields the velocity of the object the steeper the line, the greater the velocity (increased displacement in a given amount of time) if the line remains level, then velocity is constant

example examine the graph choose 2 points on the line (x, y) apply the formula:

velocity-time graphs a graph describing the motion of an object, with velocity on the vertical axis and time on the horizontal axis useful when studying objects moving with constant velocity or constant acceleration positive velocity positive velocity zero acceleration positive acceleration

shape of v-t graphs show direction: show change in velocity (acceleration)

comparing p-t and v-t graphs the following motion yields: position-time graph velocity-time graph CONSTANT VELOCITY (UNIFORM MOTION)

comparing p-t and v-t graphs the following motion yields: position-time graph velocity-time graph CHANGING VELOCITY (NON-UNIFORM MOTION)

area of a v-t graph for a velocity-time graph, the area bound by the line and the axes represents the displacement of the object

equations for area calculations recall the equations for calculating the area of basic geometric shapes note that the area of a trapezoid can be calculated by finding the sum of the areas of the contained rectangle and triangle

practice A = 30 m/s X 4 s A = 30 m/s X 3 s = 120 m = 90 m

practice A = ½ X 1 s X 10 m/s A = ½ X 3 s X 30 m/s = 5 m = 45 m

practice A = ½ x 1s x (20+30 m/s) A = ½ x 2s x (30+10) = 25 m = 40 m

Quick Quiz Consider the graph at the right. The object whose motion is represented by this graph is ... (include all that are true): moving in the positive direction. moving with a constant velocity. moving with a negative velocity. slowing down. changing directions. speeding up. moving with a positive acceleration. moving with a constant acceleration.